Global Solution Theorems for Odes
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Date
2016-08
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Addis Ababa University
Abstract
This thesis explores the globalization of the implicit function theorem (IFT) within the context of global solution theorems for ordinary differential equations (ODEs). Traditionally, the IFT provides powerful local results, but its global applicability has been less thoroughly examined. By extending the IFT to a global setting, this work develops new theoretical frameworks for understanding and solving ODEs on a broader scale. The study introduces generalized formulations of the IFT, derives significant global bifurcation results, and applies topological methods such as the Leray-Schauder degree to substantiate these results. Emphasis is placed on deriving conditions under which global solutions can be effectively analyzed and obtained.
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Keywords
Global Solution, Theorems, Odes